Question

Let a₁, a₂, a₃, a₄ and a₅be such that a₁, a₂ and a₃ are in A.P., a₂, a₃ and a₄ are in G.P. and a₃, a₄ and a₅ are in H.P. Then a₁, a₃ and a₅ are in

• A. G.P.
• B. A.P.
• C. H.P.
• D. None of these

Answer 1

Answer: (A)

G.P.

Answer 2

Since a₁, a₂, a₃ are in A.P.

\ 2a₂ = a₁ + a₃ … (1)

Since a₂, a₃, a₄ are in G.P.

\ a₃² = a₂ a₄ … (2)

Since a₂, a₄, a₅ are in H.P.

\ a₄ = $\frac { 2 a _ { 3 } a _ { 5 } } { a _ { 3 } + a _ { 5 } }$ … (3)

Putting a₂ = and a₄ = $\frac { 2 a _ { 3 } a _ { 5 } } { a _ { 3 } + a _ { 5 } }$ in (2)

We get a₃² = . $\frac { 2 a _ { 3 } a _ { 5 } } { a _ { 3 } + a _ { 5 } }$

a₃² + a₃ a₅ = a₁ a₅ + a₃ a₅

Ž a₃² = a₁ a₅ Ž a₁, a₃, a₅ are in G.P